Background

This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) Biomass growth vs. stand biomass relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.

We considered the following Michaelis-Menten functional form \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac{A \cdot StdAge}{k+StdAge}\right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(StdAge\) is the stand age at the second of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the peak growing season (June-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1960-1989), and \(yr\) is the measurement year (all FI A data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Model selection is used to determine the best fitting models, which is implemented in two parts. The first part selected the best model form using \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest) and \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period).

model 1: simple model \(B = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot StdAge} {k+StdAge} \right)\)

model 2: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot StdAge} {k+StdAge} \right)\)

Then, model selection part two takes the best fitting model from part 1 and and adds the \(p\) and \(s\) parameters (individually then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p) * A \cdot StdAge} {k+StdAge} \right)\)

sub-model b: s form \(\left( \frac {A \cdot StdAge^s} {k^s+StdAge^s} \right)\)

sub-model c: p and s together \(pA + \left( \frac {(1-p) *A \cdot StdAge^s} {k^s + StdAge^s} \right)\)

Note:

This analysis uses ALL available plot biomass data

which includes the following plot-based filtering criteria:

exclude FIA plots in plantation forests
exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9938     2556.7                                
## 2   9937     2541.4  1 15.341  59.985 1.049e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 107909.7
## 2     2 107851.8

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   -0.383270   0.101114  -3.790 0.000151 ***
## phi   0.052775   0.006569   8.034 1.05e-15 ***
## A   556.613146  34.179453  16.285  < 2e-16 ***
## k   245.186030  17.581092  13.946  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5057 on 9937 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.762e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   9937     2541.4                          
## 2   9936     2540.9  1 0.48648  1.9024 0.1678
##   model      AIC
## 1     2 107851.8
## 2    2a 107851.9
## 3    2b       NA
## 4    2c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   -0.383270   0.101114  -3.790 0.000151 ***
## phi   0.052775   0.006569   8.034 1.05e-15 ***
## A   556.613146  34.179453  16.285  < 2e-16 ***
## k   245.186030  17.581092  13.946  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5057 on 9937 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.762e-06
##   (2 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1  30370      10683                         
## 2  30361      10682  9  1.207  0.3812 0.9447
##   model      AIC
## 1     1 316873.0
## 2     2 316790.5

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.003487   0.062219   0.056    0.955    
## phi  -0.005058   0.003123  -1.620    0.105    
## A   208.607545   4.439034  46.994   <2e-16 ***
## k    91.158802   2.492202  36.578   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5932 on 30361 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.498e-06
##   (30 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: does not fit

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)    
## 1  30361      10682                              
## 2  30360      10662  1  19.84  56.491 5.8e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 316790.5
## 2    2a 316736.1
## 3    2b 316780.2
## 4    2c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   -0.023795   0.061696  -0.386     0.70    
## phi  -0.004728   0.003120  -1.516     0.13    
## A   230.695658   7.026466  32.832  < 2e-16 ***
## k   112.039694   5.271333  21.255  < 2e-16 ***
## p     0.013745   0.001721   7.985 1.45e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5926 on 30360 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.723e-06
##   (30 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1  11289     2126.3                           
## 2  11288     2126.3  1 0.027622  0.1466 0.7018
##   model      AIC
## 1     1 123755.5
## 2     2 123757.4

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.03093    0.07355  -0.421    0.674    
## A  494.44302   21.74831  22.735   <2e-16 ***
## k  158.15402    8.54362  18.511   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.434 on 11289 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.7e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: does not fit

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1  11289     2126.3                          
## 2  11288     2126.2  1 0.10645  0.5652 0.4522
##   model      AIC
## 1     1 123755.5
## 2    1a 123756.9
## 3    1b       NA
## 4    1c       NA

## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "221", , value =
## structure(list(: provided 18 variables to replace 17 variables

## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "221", , value =
## structure(list(: provided 18 variables to replace 17 variables

## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "221", , value =
## structure(list(: provided 18 variables to replace 17 variables

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.03093    0.07355  -0.421    0.674    
## A  494.44302   21.74831  22.735   <2e-16 ***
## k  158.15402    8.54362  18.511   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.434 on 11289 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.7e-06
##   (2 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   7909     2647.4                          
## 2   7908     2647.2  1 0.21999  0.6572 0.4176

##   model      AIC
## 1     1 85472.19
## 2     2 85473.53

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.2451     0.1104   -2.22   0.0264 *  
## A  528.2512    42.9834   12.29   <2e-16 ***
## k  242.8753    22.7556   10.67   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5786 on 7909 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.799e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   7909     2647.4                              
## 2   7908     2644.2  1 3.1482  9.4151 0.002159 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 85472.19
## 2    1a 85464.77
## 3    1b       NA
## 4    1c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  -0.229136   0.111317  -2.058   0.0396 *  
## A  449.068734  41.427170  10.840  < 2e-16 ***
## k  189.508155  23.529869   8.054 9.19e-16 ***
## p   -0.008452   0.003651  -2.315   0.0206 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5783 on 7908 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.275e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13436     2603.2                                
## 2  13435     2600.1  1 3.1828  16.446 5.034e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 140769.3
## 2     2 140754.9

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.059184   0.072709   0.814    0.416    
## phi  -0.018594   0.004521  -4.113 3.93e-05 ***
## A   238.276645   6.455550  36.910  < 2e-16 ***
## k    73.287908   2.872621  25.513  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4399 on 13435 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.823e-06
##   (7 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1  13435     2600.1                               
## 2  13434     2600.1  1  0.0004   0.0021 0.9635    
## 3  13434     2593.9  0  0.0000                    
## 4  13433     2571.9  1 21.9779 114.7902 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 140754.9
## 2    2a 140756.9
## 3    2b 140724.9
## 4    2c 140612.6

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.082410   0.073052   1.128 0.259296    
## phi  -0.016545   0.004501  -3.675 0.000238 ***
## A   144.478610   3.756822  38.458  < 2e-16 ***
## k    38.479465   1.013132  37.981  < 2e-16 ***
## p     0.145366   0.012293  11.825  < 2e-16 ***
## s     2.115570   0.105329  20.085  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4376 on 13433 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.699e-06
##   (7 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1  19932     6444.3                            
## 2  19931     6442.9  1 1.4098  4.3612 0.03678 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 217634.0
## 2     2 217631.6

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.635113   0.075632   8.397   <2e-16 ***
## phi  -0.008778   0.004210  -2.085   0.0371 *  
## A   273.716406   6.200726  44.143   <2e-16 ***
## k    66.637249   1.817470  36.665   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5686 on 19931 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.649e-06
##   (26 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  19931     6442.9                                 
## 2  19930     6390.5  1  52.413  163.46 < 2.2e-16 ***
## 3  19930     6434.4  0   0.000                      
## 4  19929     6321.2  1 113.247  357.04 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 217631.6
## 2    2a 217470.8
## 3    2b 217607.5
## 4    2c 217255.6

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.696041   0.076247   9.129   <2e-16 ***
## phi  -0.009557   0.004162  -2.296   0.0217 *  
## A   174.697261   4.714684  37.054   <2e-16 ***
## k    33.390061   1.183674  28.209   <2e-16 ***
## p     0.070684   0.003851  18.354   <2e-16 ***
## s     1.626479   0.045572  35.690   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5632 on 19929 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.992e-06
##   (26 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  20858     9688.4                                
## 2  20855     9677.1  3 11.326  8.1366 2.065e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 232500.8
## 2     2 232460.1

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.23827    0.07490   3.181  0.00147 ** 
## phi   0.01426    0.00516   2.763  0.00574 ** 
## A   300.75555    8.24620  36.472  < 2e-16 ***
## k    76.56971    2.56518  29.850  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6812 on 20855 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.192e-07
##   (60 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1  20855     9677.1                                 
## 2  20854     9613.9  1  63.196  137.08 < 2.2e-16 ***
## 3  20854     9664.0  0   0.000                      
## 4  20853     9549.8  1 114.204  249.38 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 232460.1
## 2    2a 232325.5
## 3    2b 232434.0
## 4    2c 232188.0

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  2.429e-01  7.416e-02   3.275  0.00106 ** 
## phi 1.507e-02  5.119e-03   2.944  0.00324 ** 
## A   1.943e+02  6.621e+00  29.353  < 2e-16 ***
## k   3.837e+01  1.793e+00  21.402  < 2e-16 ***
## p   6.184e-02  4.309e-03  14.349  < 2e-16 ***
## s   1.554e+00  5.041e-02  30.828  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6767 on 20853 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.006e-06
##   (60 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   2186     817.40                            
## 2   2185     815.82  1 1.5791  4.2294 0.03985 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 24934.44
## 2     2 24932.20

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.12226    0.23290  -0.525   0.5997    
## phi   0.03788    0.01859   2.037   0.0417 *  
## A   531.80592   74.36941   7.151 1.17e-12 ***
## k   161.97411   27.41420   5.908 4.00e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.611 on 2185 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.058e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   2185     815.82                              
## 2   2184     814.69  1 1.1257  3.0176 0.082505 . 
## 3   2184     815.53  0 0.0000                    
## 4   2183     813.00  1 2.5343  6.8049 0.009153 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 24932.20
## 2    2a 24931.18
## 3    2b 24933.42
## 4    2c 24928.61

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.13384    0.23173  -0.578   0.5636    
## phi   0.03911    0.01856   2.107   0.0352 *  
## A   315.56482   79.16136   3.986 6.93e-05 ***
## k    72.27038   23.67493   3.053   0.0023 ** 
## p     0.04870    0.02473   1.969   0.0490 *  
## s     1.45175    0.24454   5.937 3.38e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6103 on 2183 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.444e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89517, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.499, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    242     62.060                          
## 2    241     61.802  1 0.25746   1.004 0.3174

##   model      AIC
## 1     1 3072.961
## 2     2 3073.942

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   -0.5707     0.4891  -1.167 0.244465    
## A  1512.2130   452.0474   3.345 0.000953 ***
## k   283.3775    89.0654   3.182 0.001656 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5064 on 242 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.901e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    242     62.060                             
## 2    241     61.245  1 0.81471  3.2059 0.07463 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3072.961
## 2    1a 3071.723
## 3    1b       NA
## 4    1c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.58798    0.48266  -1.218 0.224336    
## A  1176.06873  341.99673   3.439 0.000688 ***
## k   176.81762   69.54297   2.543 0.011631 *  
## p    -0.02765    0.02296  -1.204 0.229626    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5041 on 241 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.632e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96346, p-value = 6.668e-06
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.2838, p-value = 0.001024
## alternative hypothesis: two.sided

predict and plot

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   2781     760.98                           
## 2   2780     760.95  1 0.034127  0.1247  0.724

##   model      AIC
## 1     1 29399.95
## 2     2 29401.83

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.3455     0.1580  -2.187   0.0289 *  
## A  303.2515    24.8271  12.215   <2e-16 ***
## k  114.1674    11.9374   9.564   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5231 on 2781 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.755e-06
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1   2781     760.98                             
## 2   2780     760.17  1 0.81064  2.9646 0.08522 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 29399.95
## 2    1a 29398.99
## 3    1b 29390.81
## 4    1c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + 
##     STDAGE^s))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.3165     0.1596  -1.983   0.0475 *  
## A  191.1468    18.4763  10.345  < 2e-16 ***
## k   50.8835     7.0584   7.209 7.23e-13 ***
## s    1.3703     0.1031  13.288  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5222 on 2780 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.049e-06
##   (3 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96263, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -24.432, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1282     497.71                           
## 2   1281     497.68  1 0.026566  0.0684 0.7938

##   model      AIC
## 1     1 13108.71
## 2     2 13110.64

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.4374     0.2635  -1.660   0.0971 .  
## A  220.2286    25.1890   8.743  < 2e-16 ***
## k   82.2162    11.9149   6.900 8.14e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6231 on 1282 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 7.21e-06
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1282     497.71                           
## 2   1281     497.69  1 0.022344  0.0575 0.8105
##   model      AIC
## 1     1 13108.71
## 2    1a 13110.66
## 3    1b 13102.40
## 4    1c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + 
##     STDAGE^s))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.4803     0.2575  -1.865   0.0624 .  
## A  134.9472    16.4694   8.194 6.07e-16 ***
## k   33.0748     5.9587   5.551 3.46e-08 ***
## s    1.4034     0.1365  10.279  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6213 on 1281 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 9.017e-06
##   (3 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94897, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -12.208, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

## Warning: Unknown or uninitialised column: `nls_weights.2`.

## Error in nls(f_1, data = P_261, start = c(ge = ge.start, A = A.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562

## Warning: Unknown or uninitialised column: `nls_weights.2`.

##   model      AIC
## 1     1       NA
## 2     2 736.1474

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)   
## ge    5.60183    6.70319   0.836  0.40715   
## phi   0.19470    0.09691   2.009  0.04974 * 
## A   566.24038  333.12863   1.700  0.09515 . 
## k   215.25516   71.78356   2.999  0.00415 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 164.3 on 52 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 6.205e-06

summary

simple model: does not fit
phi model: fits

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (only 64 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed

##   model AIC
## 1     1  NA
## 2     2  NA

## Warning in min(AIC1_262$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_262.' not found

summary

simple model: does not fit
phi model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (0 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    426     98.090                            
## 2    425     97.026  1 1.0635  4.6584 0.03146 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 5410.292
## 2     2 5407.615

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.29301    0.68606   1.885   0.0602 .  
## phi   -0.08221    0.03786  -2.171   0.0305 *  
## A   1049.16808  209.39393   5.010 7.98e-07 ***
## k    224.28333   45.52407   4.927 1.20e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4778 on 425 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.113e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_263,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    425     97.026                          
## 2    424     96.827  1 0.19956  0.8739 0.3504
##   model      AIC
## 1     2 5407.615
## 2    2a 5408.732
## 3    2b 5404.762
## 4    2c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (A * STDAGE^s/(k^s + STDAGE^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   1.558e+00  7.516e-01   2.073   0.0388 *  
## phi -6.898e-02  3.817e-02  -1.807   0.0715 .  
## A    5.777e+03  1.342e+04   0.430   0.6672    
## k    4.975e+03  1.915e+04   0.260   0.7952    
## s    7.450e-01  1.037e-01   7.185 3.04e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4757 on 424 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 2.064e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97891, p-value = 6.856e-06
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.8867, p-value = 3.94e-09
## alternative hypothesis: two.sided

predict and plot

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    503     197.73                            
## 2    502     196.55  1 1.1824  3.0198 0.08287 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 5500.917
## 2     2 5499.883

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.74878    0.45224  -1.656 0.098404 .  
## phi  -0.06604    0.04231  -1.561 0.119148    
## A   198.37376   34.24510   5.793 1.22e-08 ***
## k   126.91926   32.37995   3.920 0.000101 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6257 on 502 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.528e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    502     196.55                          
## 2    501     196.12  1 0.42914  1.0963 0.2956
##   model      AIC
## 1     2 5499.883
## 2    2a 5500.777
## 3    2b       NA
## 4    2c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.74878    0.45224  -1.656 0.098404 .  
## phi  -0.06604    0.04231  -1.561 0.119148    
## A   198.37376   34.24510   5.793 1.22e-08 ***
## k   126.91926   32.37995   3.920 0.000101 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6257 on 502 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.528e-06
##   (2 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89169, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.5305, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

## Warning: Unknown or uninitialised column: `nls_weights.2`.
## Unknown or uninitialised column: `nls_weights.2`.

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1     13     3559.6                         
## 2     12     3499.8  1 59.729  0.2048  0.659

##   model      AIC
## 1     1 139.8829
## 2     2 141.6121

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)
## ge   -1.737      1.176  -1.477    0.163
## A   119.386    102.105   1.169    0.263
## k   101.084    115.067   0.878    0.396
## 
## Residual standard error: 16.55 on 13 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 9.662e-06

summary

simple model: fits
phi model: fits

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

## Error in nls(f_1, data = P_321, start = c(ge = ge.start, A = A.start,  : 
##   singular gradient

## Error in nls(f_2, data = P_321, start = c(ge = ge.start, phi = phi.start,  : 
##   singular gradient

##   model AIC
## 1     1  NA
## 2     2  NA

## Warning in min(AIC1_321$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_321.' not found

summary

simple model: does not fit
phi model: does not fit

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

## Warning: Unknown or uninitialised column: `nls_weights.2`.
## Unknown or uninitialised column: `nls_weights.2`.

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1      5     5487.1                         
## 2      4     5479.9  1 7.2366  0.0053 0.9456

##   model      AIC
## 1     1 82.94879
## 2     2 84.93823

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge    3.598     13.618   0.264   0.8022  
## A    20.616     37.917   0.544   0.6100  
## k   -78.208     32.792  -2.385   0.0628 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 33.13 on 5 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.894e-06

summary

simple model: fits
phi model: fits

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

Cannot fit model
not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    749     502.27                         
## 2    748     500.96  1 1.3185  1.9687  0.161

##   model      AIC
## 1     1 7643.027
## 2     2 7643.050

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.3773     0.5245  -0.719    0.472    
## A  111.0018    18.8722   5.882 6.12e-09 ***
## k   78.2492    16.6590   4.697 3.14e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8189 on 749 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 7.308e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    749     502.27                                
## 2    748     501.49  1  0.786  1.1724    0.2793    
## 3    748     502.02  0  0.000                      
## 4    747     489.77  1 12.249 18.6829 1.753e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7643.027
## 2    1a 7643.849
## 3    1b 7644.646
## 4    1c 7628.070

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge -0.15646    0.56610  -0.276 0.782335    
## A  58.03452    7.69556   7.541 1.35e-13 ***
## k  33.19091    3.02797  10.961  < 2e-16 ***
## p   0.18739    0.03023   6.199 9.39e-10 ***
## s   3.92007    1.13605   3.451 0.000591 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8097 on 747 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.363e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.86401, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -12.021, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

* Cannot fit model

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    319     225.08                          
## 2    318     224.66  1 0.41885  0.5929 0.4419

##   model      AIC
## 1     1 3495.454
## 2     2 3496.854

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge  -0.2726     0.8399  -0.325   0.7457  
## A  221.7114   101.3257   2.188   0.0294 *
## k  111.7604    64.6879   1.728   0.0850 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.84 on 319 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.338e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = P_332,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = P_332,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    319     225.08                         
## 2    317     222.68  2 2.4005  1.7086 0.1828
##   model      AIC
## 1     1 3495.454
## 2    1a       NA
## 3    1b       NA
## 4    1c 3496.001

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge  -0.2726     0.8399  -0.325   0.7457  
## A  221.7114   101.3257   2.188   0.0294 *
## k  111.7604    64.6879   1.728   0.0850 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.84 on 319 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.338e-06
##   (2 observations deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.84817, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.635, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1    143     47.408                            
## 2    142     47.404  1 0.0038133  0.0114  0.915

##   model      AIC
## 1     1 1571.465
## 2     2 1573.453

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)   
## ge    1.456      1.492   0.976  0.33092   
## A   167.149     63.483   2.633  0.00939 **
## k   137.477     57.992   2.371  0.01909 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5758 on 143 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.806e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    143     47.408                          
## 2    142     47.292  1 0.11632  0.3493 0.5555
##   model      AIC
## 1     1 1571.465
## 2    1a 1573.107
## 3    1b 1572.451
## 4    1c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)   
## ge    1.456      1.492   0.976  0.33092   
## A   167.149     63.483   2.633  0.00939 **
## k   137.477     57.992   2.371  0.01909 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5758 on 143 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.806e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97471, p-value = 0.008393
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.7953, p-value = 0.0001475
## alternative hypothesis: two.sided

predict and plot

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    316     248.86                         
## 2    315     247.20  1 1.6645  2.1211 0.1463

##   model      AIC
## 1     1 3398.076
## 2     2 3397.935

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.40249    0.86776  -0.464 0.643092    
## phi -0.08326    0.06173  -1.349 0.178367    
## A   93.05864   24.23433   3.840 0.000149 ***
## k   57.11574   19.87840   2.873 0.004339 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8859 on 315 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.331e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    315     247.20                              
## 2    314     246.66  1 0.5323  0.6776 0.411031   
## 3    314     245.51  0 0.0000                    
## 4    313     237.31  1 8.1965 10.8108 0.001124 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 3397.935
## 2    2a 3399.247
## 3    2b 3397.748
## 4    2c 3388.916

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.17078    0.93933  -0.182  0.85585    
## phi -0.09125    0.06151  -1.483  0.13895    
## A   61.58942   14.70342   4.189 3.65e-05 ***
## k   45.99393    8.86531   5.188 3.83e-07 ***
## p    0.26680    0.08890   3.001  0.00291 ** 
## s    3.40745    1.74208   1.956  0.05136 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8707 on 313 degrees of freedom
## 
## Number of iterations to convergence: 19 
## Achieved convergence tolerance: 9.465e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87835, p-value = 3.319e-15
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.3789, p-value = 7.496e-08
## alternative hypothesis: two.sided

predict and plot

plotting 2

411 - Everglades

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    166     71.634                                
## 2    165     67.027  1 4.6065   11.34 0.0009441 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 1787.685
## 2     2 1778.452

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    -1.7989     0.4433  -4.058 7.62e-05 ***
## phi   -0.3428     0.1230  -2.786  0.00596 ** 
## A   1605.1761  3041.3144   0.528  0.59835    
## k    764.0349  1516.4489   0.504  0.61505    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6374 on 165 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.365e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = P_411,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = P_411,  : 
##   singular gradient
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_411,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model      AIC
## 1     2 1778.452
## 2    2a       NA
## 3    2b       NA
## 4    2c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    -1.7989     0.4433  -4.058 7.62e-05 ***
## phi   -0.3428     0.1230  -2.786  0.00596 ** 
## A   1605.1761  3041.3144   0.528  0.59835    
## k    764.0349  1516.4489   0.504  0.61505    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6374 on 165 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 3.365e-06
##   (1 observation deleted due to missingness)

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97702, p-value = 0.006624
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.826, p-value = 1.393e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  10057     2001.3                                
## 2  10056     1994.5  1 6.8491  34.532 4.325e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 107037.0
## 2     2 107004.5

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  8.733e-02  9.286e-02    0.94    0.347    
## phi 3.115e-02  5.504e-03    5.66 1.56e-08 ***
## A   4.790e+02  2.391e+01   20.03  < 2e-16 ***
## k   2.205e+02  1.280e+01   17.23  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4454 on 10056 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.401e-06
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  10056     1994.5                                
## 2  10055     1987.0  1 7.4779  37.841 7.967e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 107004.5
## 2    2a 106968.7
## 3    2b       NA
## 4    2c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.054423   0.091634   0.594    0.553    
## phi   0.030372   0.005481   5.541 3.08e-08 ***
## A   377.503856  20.268188  18.625  < 2e-16 ***
## k   144.875032  12.158229  11.916  < 2e-16 ***
## p    -0.021206   0.004829  -4.391 1.14e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4445 on 10055 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.957e-06
##   (3 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  13160     2210.7                                
## 2  13159     2191.1  1 19.627  117.87 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 145414.7
## 2     2 145299.3

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.548961   0.071191   7.711 1.34e-14 ***
## phi  -0.038971   0.003549 -10.980  < 2e-16 ***
## A   271.111248   6.089184  44.523  < 2e-16 ***
## k    63.850565   2.100846  30.393  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4081 on 13159 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.803e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1  13159     2191.1                              
## 2  13158     2191.0  1  0.052   0.3099 0.5777    
## 3  13158     2178.8  0  0.000                    
## 4  13157     2146.2  1 32.590 199.7893 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 145299.3
## 2    2a 145301.0
## 3    2b 145227.4
## 4    2c 145031.0

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.642941   0.073275   8.774   <2e-16 ***
## phi  -0.037296   0.003508 -10.631   <2e-16 ***
## A   170.328853   3.502018  48.637   <2e-16 ***
## k    37.150549   0.741208  50.122   <2e-16 ***
## p     0.165317   0.009961  16.596   <2e-16 ***
## s     2.342576   0.099384  23.571   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4039 on 13157 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.84e-06
##   (2 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1243     169.25                                
## 2   1242     166.62  1 2.6234  19.555 1.063e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 12649.64
## 2     2 12632.18

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.52664    0.15034  -3.503 0.000476 ***
## phi   0.06689    0.01592   4.202 2.84e-05 ***
## A   271.29836   24.43298  11.104  < 2e-16 ***
## k    83.42650   11.61984   7.180 1.20e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3663 on 1242 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.432e-06
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1242     166.62                           
## 2   1241     166.59  1 0.035854  0.2671 0.6054
## 3   1241     166.55  0 0.000000               
## 4   1240     166.53  1 0.028854  0.2149 0.6431
##   model      AIC
## 1     2 12632.18
## 2    2a 12633.91
## 3    2b 12633.65
## 4    2c 12635.43

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.52664    0.15034  -3.503 0.000476 ***
## phi   0.06689    0.01592   4.202 2.84e-05 ***
## A   271.29836   24.43298  11.104  < 2e-16 ***
## k    83.42650   11.61984   7.180 1.20e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3663 on 1242 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.432e-06
##   (2 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97257, p-value = 1.24e-14
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -17.49, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1   1484     342.22                             
## 2   1483     341.30  1 0.92221  4.0072 0.04549 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 15286.15
## 2     2 15284.13

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.15481    0.24948   0.621   0.5350    
## phi   0.03631    0.01849   1.964   0.0497 *  
## A   316.03672   38.38330   8.234 3.94e-16 ***
## k   142.92057   21.27357   6.718 2.61e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4797 on 1483 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.777e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1483     341.30                           
## 2   1482     341.24  1 0.055697  0.2419 0.6229
## 3   1482     341.20  0 0.000000               
## 4   1481     341.19  1 0.008313  0.0361 0.8494
##   model      AIC
## 1     2 15284.13
## 2    2a 15285.89
## 3    2b 15285.71
## 4    2c 15287.68

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.15481    0.24948   0.621   0.5350    
## phi   0.03631    0.01849   1.964   0.0497 *  
## A   316.03672   38.38330   8.234 3.94e-16 ***
## k   142.92057   21.27357   6.718 2.61e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4797 on 1483 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.777e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96927, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.614, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   7934     4843.9                          
## 2   7933     4843.0  1 0.86271  1.4131 0.2346

##   model      AIC
## 1     1 105723.9
## 2     2 105724.4

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   0.02465    0.16455    0.15    0.881    
## A  780.98344   41.40997   18.86   <2e-16 ***
## k  223.08680   12.70480   17.56   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7814 on 7934 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.343e-06
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   7934     4843.9                                 
## 2   7933     4825.5  1 18.4033 30.2546 3.907e-08 ***
## 3   7932     4825.3  1  0.1519  0.2497    0.6173    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 105723.9
## 2    1a 105695.6
## 3    1b       NA
## 4    1c 105697.4

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   0.008305   0.163098   0.051    0.959    
## A  682.531690  36.459330  18.720  < 2e-16 ***
## k  159.113169  12.652352  12.576  < 2e-16 ***
## p   -0.033932   0.007527  -4.508 6.63e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7799 on 7933 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.717e-07
##   (3 observations deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: fits

plot residuals

predict and plot

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4571     2296.8                                
## 2   4570     2264.8  1 32.069  64.711 1.096e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 57841.68
## 2     2 57779.37

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    2.35377    0.46352   5.078 3.96e-07 ***
## phi   0.10652    0.01124   9.476  < 2e-16 ***
## A   355.35507   27.88660  12.743  < 2e-16 ***
## k   148.96824   12.01719  12.396  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.704 on 4570 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.649e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   4570     2264.8                          
## 2   4569     2264.4  1 0.33289  0.6717 0.4125
## 3   4569     2264.7  0 0.00000               
## 4   4568     2264.2  1 0.49094  0.9905 0.3197
##   model      AIC
## 1     2 57779.37
## 2    2a 57780.69
## 3    2b 57781.25
## 4    2c 57782.26

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    2.35377    0.46352   5.078 3.96e-07 ***
## phi   0.10652    0.01124   9.476  < 2e-16 ***
## A   355.35507   27.88660  12.743  < 2e-16 ***
## k   148.96824   12.01719  12.396  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.704 on 4570 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.649e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91632, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -25.825, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

model selection 1

## Warning: Unknown or uninitialised column: `nls_weights.2`.

## Error in nls(f_1, data = P_M262, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50

## Warning: Unknown or uninitialised column: `nls_weights.2`.

##   model      AIC
## 1     1       NA
## 2     2 615.3221

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   -1.8417     0.8477  -2.172  0.03459 *  
## phi  -0.3664     0.2019  -1.814  0.07561 .  
## A    84.9819    25.1232   3.383  0.00140 ** 
## k   -22.9322     5.4606  -4.200  0.00011 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 68.33 on 50 degrees of freedom
## 
## Number of iterations to convergence: 23 
## Achieved convergence tolerance: 6.694e-06

summary

simple model: does not fit
phi model: fits

model selection 2

summary

add p model: does not fit
add s model: does not fit
add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    909     284.47                          
## 2    908     284.00  1 0.46904  1.4996  0.221

##   model      AIC
## 1     1 9555.938
## 2     2 9556.433

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.9439     0.2374  -3.977 7.54e-05 ***
## A  393.0871    93.6950   4.195 2.99e-05 ***
## k  282.2375    85.6482   3.295  0.00102 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5594 on 909 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.158e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    909     284.47                          
## 2    908     284.31  1 0.16139  0.5154  0.473
##   model      AIC
## 1     1 9555.938
## 2    1a 9557.420
## 3    1b       NA
## 4    1c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.9439     0.2374  -3.977 7.54e-05 ***
## A  393.0871    93.6950   4.195 2.99e-05 ***
## k  282.2375    85.6482   3.295  0.00102 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5594 on 909 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.158e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: does not fit
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9539, p-value = 2.596e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.6403, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   5206     1821.1                          
## 2   5205     1820.9  1 0.24737  0.7071 0.4004

##   model      AIC
## 1     1 54709.07
## 2     2 54710.37

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.97977    0.09812  -9.986   <2e-16 ***
## A  283.57736   14.79752  19.164   <2e-16 ***
## k  163.79765   11.57994  14.145   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5915 on 5206 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.7e-07
##   (27 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value   Pr(>F)    
## 1   5206     1821.1                                
## 2   5205     1817.8  1  3.3414  9.5675 0.001991 ** 
## 3   5205     1820.9  0  0.0000                     
## 4   5204     1802.1  1 18.7736 54.2133 2.08e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 54709.07
## 2    1a 54701.51
## 3    1b 54710.31
## 4    1c 54658.33

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - 
##     p) * A * STDAGE^s/(k^s + STDAGE^s)))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -1.00006    0.09689 -10.322   <2e-16 ***
## A  171.04159    8.60367  19.880   <2e-16 ***
## k   82.71515    4.09588  20.195   <2e-16 ***
## p    0.13600    0.01413   9.626   <2e-16 ***
## s    2.13334    0.17553  12.154   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5885 on 5204 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 6.463e-06
##   (27 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: fits

plot residuals

predict and plot

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6772     3204.3                                
## 2   6771     3190.9  1 13.434  28.508 9.634e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 73901.46
## 2     2 73875.00

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  3.504e-01  1.856e-01   1.888   0.0591 .  
## phi 5.170e-02  9.073e-03   5.698 1.26e-08 ***
## A   2.253e+02  1.175e+01  19.184  < 2e-16 ***
## k   1.453e+02  8.485e+00  17.129  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6865 on 6771 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.071e-06
##   (5 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1   6771     3190.9                            
## 2   6770     3188.6  1 2.2882  4.8583 0.02755 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     2 73875.00
## 2    2a 73872.14
## 3    2b 73873.04
## 4    2c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  3.328e-01  1.846e-01   1.803   0.0715 .  
## phi 5.299e-02  9.054e-03   5.852 5.08e-09 ***
## A   2.401e+02  1.620e+01  14.816  < 2e-16 ***
## k   1.656e+02  1.637e+01  10.115  < 2e-16 ***
## p   8.549e-03  3.898e-03   2.193   0.0283 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6863 on 6770 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 8.081e-06
##   (5 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

predict and plot

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4434     1963.5                                
## 2   4433     1953.8  1 9.7019  22.012 2.791e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

##   model      AIC
## 1     1 49716.85
## 2     2 49696.87

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.31327    0.23183   1.351    0.177    
## phi   0.05343    0.01098   4.867 1.17e-06 ***
## A   353.28995   25.05730  14.099  < 2e-16 ***
## k   185.81962   13.58745  13.676  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6639 on 4433 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.849e-06
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1   4433     1953.8                            
## 2   4432     1953.8  1 0.0054658  0.0124 0.9113
##   model      AIC
## 1     2 49696.87
## 2    2a 49698.86
## 3    2b 49654.37
## 4    2c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (A * STDAGE^s/(k^s + STDAGE^s))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.31425    0.23062   1.363    0.173    
## phi   0.04752    0.01103   4.309 1.67e-05 ***
## A   227.37954   17.22538  13.200  < 2e-16 ***
## k    82.08926    8.13709  10.088  < 2e-16 ***
## s     1.29097    0.04711  27.405  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6606 on 4432 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 8.711e-06
##   (3 observations deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93128, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -19.5, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    712     278.71                         
## 2    711     277.68  1 1.0259  2.6267 0.1055

##   model      AIC
## 1     1 7183.953
## 2     2 7183.316

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     A * STDAGE/(k + STDAGE)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.26900    0.39205  -0.686    0.493    
## phi   0.03120    0.01943   1.606    0.109    
## A   119.13429   17.23489   6.912 1.06e-11 ***
## k    74.13118   16.35263   4.533 6.81e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6249 on 711 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.953e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_M334,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    711     277.68                          
## 2    710     277.10  1 0.57808  1.4812  0.224
##   model      AIC
## 1     2 7183.316
## 2    2a 7183.826
## 3    2b 7183.207
## 4    2c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (A * STDAGE^s/(k^s + STDAGE^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)   
## ge  -3.571e-01  3.791e-01  -0.942  0.34650   
## phi  3.184e-02  1.944e-02   1.638  0.10194   
## A    6.329e+02  2.290e+03   0.276  0.78232   
## k    3.062e+03  2.373e+04   0.129  0.89734   
## s    6.114e-01  2.046e-01   2.988  0.00291 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6245 on 710 degrees of freedom
## 
## Number of iterations to convergence: 25 
## Achieved convergence tolerance: 4.116e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95815, p-value = 2.115e-13
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.5121, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1    488     183.51                            
## 2    487     183.50  1 0.0097364  0.0258 0.8724

##   model      AIC
## 1     1 4999.077
## 2     2 5001.051

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -1.4407     0.2497  -5.769 1.42e-08 ***
## A  281.4947    47.5575   5.919 6.11e-09 ***
## k  196.9458    45.4153   4.337 1.76e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6132 on 488 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.962e-06
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    488     183.51                           
## 2    487     183.48  1 0.030432  0.0808 0.7764
##   model      AIC
## 1     1 4999.077
## 2    1a 5000.996
## 3    1b 5000.193
## 4    1c       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + 
##     STDAGE)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -1.4407     0.2497  -5.769 1.42e-08 ***
## A  281.4947    47.5575   5.919 6.11e-09 ***
## k  196.9458    45.4153   4.337 1.76e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6132 on 488 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.962e-06
##   (1 observation deleted due to missingness)

summary

add p model: fits
add s model: fits
add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92528, p-value = 6.539e-15
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.105, p-value = 1.028e-09
## alternative hypothesis: two.sided

predict and plot

plotting 2

Fitted parameters

Best / selected models by ecoprovince

Code	Ecoregion	Sel.Mod
211	Northeastern Mixed Forest	2
212	Laurentian Mixed Forest	2a
221	Eastern Broadleaf Forest	1
222	Midwest Broadleaf Forest	1a
223	Central Interior Broadleaf Forest	2c
231	Southeastern Mixed Forest	2c
232	Outer Coastal Plain Mixed Forest	2c
234	Lower Mississippi Riverine Forest	2c
242	Pacific Lowland Mixed Forest	1a
251	Prairie Parkland (Temperate)	1b
255	Prairie Parkland (Subtropical)	1b
261	California Coastal Chaparral Forest and Shrub	NA
262	California Dry Steppe	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	2b
313	Colorado Plateau Semi-Desert	2
315	Southwest Plateau and Plains Dry Steppe and Shrub	NA
321	Chihuahuan Semi-Desert	NA
322	American Semidesert and Desert	NA
331	Great Plains/Palouse Dry Steppe	1c
332	Great Plains Steppe	1
341	Intermountain Semi-Desert and Desert	1
342	Intermountain Semi-Desert	2c
411	Everglades	2
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	2a
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	2c
M223	Ozark Broadleaf Forest Meadow	2
M231	Ouachita Mixed Forest	2
M242	Cascade Mixed Forest	1a
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	2
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	1
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	1c
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	2a
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	2b
M334	Black Hills Coniferous Forest	2b
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	1

table by ecoprovince

Code	Ecoregion	region	n.obs	n.plots	ge	ge.2.5	ge.97.5	phi	phi.2.5	phi.97.5	A	A.2.5	A.97.5	k	k.2.5	k.97.5
211	Northeastern Mixed Forest	east	9943	3257	-0.3832704	-0.5814740	-0.1850667	0.0527751	0.0398982	0.0656519	556.61315	489.61449	623.61180	245.18603	210.72352	279.64853
212	Laurentian Mixed Forest	east	30395	11945	-0.0237945	-0.1447212	0.0971322	-0.0047284	-0.0108434	0.0013866	230.69566	216.92349	244.46783	112.03969	101.70766	122.37173
221	Eastern Broadleaf Forest	east	11294	4269	-0.0309342	-0.1750956	0.1132271	NA	NA	NA	494.44302	451.81253	537.07350	158.15402	141.40703	174.90101
222	Midwest Broadleaf Forest	east	7913	3189	-0.2291358	-0.4473468	-0.0109248	NA	NA	NA	449.06873	367.86054	530.27693	189.50815	143.38340	235.63291
223	Central Interior Broadleaf Forest	east	13446	4895	0.0824103	-0.0607820	0.2256026	-0.0165446	-0.0253681	-0.0077211	144.47861	137.11471	151.84251	38.47946	36.49358	40.46535
231	Southeastern Mixed Forest	east	19961	7904	0.6960411	0.5465897	0.8454924	-0.0095572	-0.0177145	-0.0013999	174.69726	165.45609	183.93843	33.39006	31.06996	35.71016
232	Outer Coastal Plain Mixed Forest	east	20919	9046	0.2428901	0.0975352	0.3882451	0.0150706	0.0050373	0.0251038	194.33256	181.35574	207.30937	38.36687	34.85302	41.88072
234	Lower Mississippi Riverine Forest	east	2190	937	-0.1338393	-0.5882767	0.3205981	0.0391064	0.0027170	0.0754959	315.56482	160.32533	470.80430	72.27038	25.84263	118.69814
242	Pacific Lowland Mixed Forest	pacific	246	172	-0.5879779	-1.5387448	0.3627890	NA	NA	NA	1176.06873	502.38434	1849.75311	176.81762	39.82798	313.80727
251	Prairie Parkland (Temperate)	east	2787	1036	-0.3164920	-0.6294917	-0.0034924	NA	NA	NA	191.14680	154.91806	227.37554	50.88350	37.04335	64.72365
255	Prairie Parkland (Subtropical)	pacific	1288	659	-0.4803010	-0.9854995	0.0248975	NA	NA	NA	134.94717	102.63716	167.25718	33.07476	21.38485	44.76466
261	California Coastal Chaparral Forest and Shrub	pacific	56	34	0.2076552	-2.1013650	2.5166754	NA	NA	NA	905.78231	218.48732	1593.07729	148.48112	17.92535	279.03690
262	California Dry Steppe	pacific	0	0	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	pacific	430	274	1.5578428	0.0805959	3.0350898	-0.0689772	-0.1440026	0.0060482	5776.56204	-20609.55325	32162.67732	4974.62963	-32664.27955	42613.53881
313	Colorado Plateau Semi-Desert	interior west	508	312	-0.7487763	-1.6372862	0.1397335	-0.0660397	-0.1491570	0.0170777	198.37376	131.09239	265.65513	126.91926	63.30235	190.53618
315	Southwest Plateau and Plains Dry Steppe and Shrub	interior west	16	12	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
321	Chihuahuan Semi-Desert	interior west	22	14	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
322	American Semidesert and Desert	interior west	8	5	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
331	Great Plains/Palouse Dry Steppe	interior west	753	473	-0.1564570	-1.2677922	0.9548782	NA	NA	NA	58.03452	42.92702	73.14201	33.19091	27.24656	39.13526
332	Great Plains Steppe	interior west	324	152	-0.2725730	-1.9249635	1.3798175	NA	NA	NA	221.71144	22.36042	421.06247	111.76036	-15.50845	239.02916
341	Intermountain Semi-Desert and Desert	interior west	147	93	1.4555092	-1.4936094	4.4046278	NA	NA	NA	167.14943	41.66251	292.63635	137.47725	22.84471	252.10980
342	Intermountain Semi-Desert	interior west	320	222	-0.1707774	-2.0189835	1.6774286	-0.0912500	-0.2122765	0.0297764	61.58942	32.65939	90.51945	45.99393	28.55079	63.43707
411	Everglades	east	170	86	-1.7989037	-2.6741478	-0.9236597	-0.3427743	-0.5857159	-0.0998326	1605.17611	-4399.73383	7610.08604	764.03493	-2230.11106	3758.18093
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	east	10063	3398	0.0544232	-0.1251974	0.2340437	0.0303723	0.0196282	0.0411165	377.50386	337.77416	417.23356	144.87503	121.04247	168.70759
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	east	13165	4970	0.6429412	0.4993110	0.7865714	-0.0372962	-0.0441726	-0.0304197	170.32885	163.46439	177.19331	37.15055	35.69767	38.60342
M223	Ozark Broadleaf Forest Meadow	east	1248	392	-0.5266414	-0.8215878	-0.2316950	0.0668924	0.0356599	0.0981250	271.29836	223.36389	319.23283	83.42650	60.62982	106.22317
M231	Ouachita Mixed Forest	east	1488	574	0.1548055	-0.3345582	0.6441691	0.0363124	0.0000483	0.0725765	316.03672	240.74538	391.32806	142.92057	101.19107	184.65006
M242	Cascade Mixed Forest	pacific	7940	4900	0.0083049	-0.3114107	0.3280205	NA	NA	NA	682.53169	611.06181	754.00157	159.11317	134.31123	183.91511
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	pacific	4575	2761	2.3537716	1.4450510	3.2624922	0.1065227	0.0844846	0.1285608	355.35507	300.68386	410.02629	148.96824	125.40875	172.52773
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	interior west	54	38	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	913	563	-0.9439044	-1.4097324	-0.4780764	NA	NA	NA	393.08713	209.20346	576.97081	282.23750	114.14629	450.32871
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	5236	3514	-1.0000591	-1.1899993	-0.8101190	NA	NA	NA	171.04159	154.17477	187.90840	82.71515	74.68551	90.74479
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	6780	4293	0.3327526	-0.0291287	0.6946338	0.0529865	0.0352378	0.0707352	240.08218	208.31663	271.84773	165.60474	133.50915	197.70032
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	4440	2838	0.3142512	-0.1378781	0.7663805	0.0475228	0.0259014	0.0691443	227.37954	193.60919	261.14989	82.08926	66.13650	98.04201
M334	Black Hills Coniferous Forest	interior west	716	364	-0.3571166	-1.1014022	0.3871690	0.0318412	-0.0063321	0.0700145	632.93389	-3862.80228	5128.67006	3062.18270	-43518.70707	49643.07246
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	interior west	492	287	-1.4406677	-1.9313520	-0.9499835	NA	NA	NA	281.49475	188.05202	374.93748	196.94578	107.71211	286.17946

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map #2

plot phi (effect of DeltaPDSI)

plot A (asymptote of B)

## Warning: Removed 7 rows containing missing values (geom_point).

plot k (stand age at half biomass asymptote)

## Warning: Removed 7 rows containing missing values (geom_point).

Calculations - weighted averages

ge (stand biomass enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US   0.1591839
## 2       pacific   0.7449677
## 3          east   0.1495858
## 4 interior west  -0.1912246

phi (effect of DeltaPDSI)

##          region weighted.phi
## 1     entire US  0.008674616
## 2       pacific  0.031273796
## 3          east  0.001203679
## 4 interior west  0.025270797

A (asymptote of forest biomass in Mg/ha)

##          region weighted.A
## 1     entire US   310.7201
## 2       pacific   707.9920
## 3          east   268.4563
## 4 interior west     0.0000

K (stand age at half maturation in years)

##          region weighted.k
## 1     entire US   134.3730
## 2       pacific   296.7343
## 3          east    92.9108
## 4 interior west   201.8142

Calculations - weighted averages subsetted to 15 ecoprovinces

211, 212, 221, 223, 231, 232, 234, 251, M211, M221, M223, M231, M242, M261, M332,

ge

##          region weighted.ge
## 1     entire US   0.2665799
## 2       pacific   0.8536036
## 3          east   0.1757210
## 4 interior west   0.3327526

phi

##          region weighted.phi
## 1     entire US  0.009575266
## 2       pacific  0.038390439
## 3          east  0.001838774
## 4 interior west  0.052986482

FIA - NLS Models: Biomass vs. Stand Age

JAH

2022-10-25

Background

211 - Northeastern Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

model selection 2

summary

plot residuals

predict and plot

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

summary

model selection 2